Question

the denominator of a fraction is two more than its numerator. if one is added to both ,then the fraction reduces to 4/5.find the original fraction ​

Answer 1

$\underline{\underline{\huge{\gray{\tt{\textbf Answer :-}}}}}$

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$\sf\large\bold{\orange{\underline{\blue{ Given :-}}}}$

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• The denominator of a fraction is two more than its numerator

• If one is added to both then the fraction reduces to 4/5

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$\sf\large\bold{\orange{\underline{\blue{ To \: Find :-}}}}$

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• Original fraction

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$\sf\large\bold{\orange{\underline{\blue{ Solution :-}}}}$

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• Let the numerator of fraction be "n"

• Let the denominator of fraction be "d"

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$\underline{\bold{\texttt{Original fraction :}}}$

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➠ $\sf \dfrac { n } { d }$ ⚊⚊⚊⚊ ⓵

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Given that , the denominator of a fraction is two more than its numerator

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So,

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➜ d = n + 2 ⚊⚊⚊⚊ ⓶

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$\underline{\bold{\texttt{Adding 1 to numerator :}}}$

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➜ n + 1 ⚊⚊⚊⚊ ⓷

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$\underline{\bold{\texttt{Adding 1 to denominator :}}}$

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➜ d + 1 ⚊⚊⚊⚊ ⓸

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Also given that , If one is added to both then the fraction reduces to 4/5

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Thus,

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From ⓷ & ⓸

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➜ $\sf \dfrac { n + 1 } { d + 1 } = \dfrac { 4 } { 5 }$

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➜ 5(n + 1) = 4(d + 1)

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➜ 5n + 5 = 4d + 4

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➜ 5n - 4d = 4 - 5 ⚊⚊⚊⚊ ⓹

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⟮ Putting d = n + 2 from ⓶ to ⓹ ⟯

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➜ 5n - 4(n + 2) = 4 - 5

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➜ 5n - 4n - 8 = -1

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➜ n = -1 + 8

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➜ n = 7 ⚊⚊⚊⚊ ⓺

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• Hence the numerator is 7

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⟮ Putting n = 7 from ⓺ to ⓶ ⟯

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➜ d = n + 2

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➜ d = 7 + 2

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➜ d = 9 ⚊⚊⚊⚊ ⓻

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• Hence the denominator is 9

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⟮ Putting n = 7 from ⓺ & d = 9 from ⓻ to equation ⓵ ⟯

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➜ $\sf \dfrac { n } { d }$

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➨ $\sf \dfrac { 7} { 9}$

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• $\rm Hence \: the \: original \: fraction \: is\: \dfrac { 7} { 9}$

Answer 2

$\Large{\underbrace{\sf{\red{Required\:Solution:}}}}$

Given :

• The denominator of α frαction is two more thαn its numerαtor.
• One is αdded to both, then the frαction reduces to 4/5.

To Find :

• The originαl frαction.

Procedure :

In this question, firstly we'll αssume the numerator to be x αnd denominator to be x+2.

Then we'll write it as fraction αnd αdd 1 to both numerαtor αnd denominαtor αnd put 4/5 equivalent to it. After thαt, we'll simplify the equαtion αnd find the vαlues of numerαtor αnd denominator. And we'll done! :D

So let's do it!

Step by step explαnαtion :

Let the numerαtor be x. so, the denominαtor will be x + 2.

According to the question,

$\implies{\sf{ \dfrac{x + 1}{ (x+2)+1} = \dfrac{4}{5}}}$

• Do cross multiplicαtion.

$\implies{\sf{ 5(x+1) = 4(x+3)}}$

• Simplify this.

$\implies{\sf{ 5x + 5 = 4x + 12}}$

$\implies{\sf{ 5x - 4x = 12 - 5}}$

$\implies{\sf{ x = 7}}$

Therefore, the frαction will be $\displaystyle{\boxed{\sf{\red{\dfrac{ 7}{9}}}}}$

And we αre done! :D

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